We consider the TRS containing the following rules:
| a | → | b | (1) |
| a | → | f(a) | (2) |
| b | → | f(f(b)) | (3) |
| f(f(f(b))) | → | b | (4) |
The underlying signature is as follows:
{a/0, b/0, f/1}To prove that the TRS is (non-)confluent, we show (non-)confluence of the following modified system:
| f(f(f(b))) | → | b | (4) |
| b | → | f(f(b)) | (3) |
| a | → | f(a) | (2) |
| a | → | b | (1) |
| f(a) | → | f(f(b)) | (5) |
All redundant rules that were added or removed can be simulated in 2 steps .